TUCSON, Ariz. (AP) Todd Graham spent months talking to fans about what they wanted in his first season as Arizona State's coach.

Their top priority: Beat Arizona.

The Sun Devils did just that, with a touch of flair to boot.

Adding an unexpected chapter to what's become a wild rivalry, Arizona State scored 24 points in the fourth quarter to beat Arizona 41-34 Friday night and help Graham land the first blow against Wildcats coach Rich Rodriguez.

``This is THE game, the most important things for us,'' said Graham, who shared the Territorial Cup trophy with former Sun Devils coach Frank Kush in the locker room. ``It wasn't just big to win, but how we won the game.''

It was pretty impressive.

Trailing 27-17 after Arizona scored 18 points in the third quarter, the Sun Devils (7-5, 5-4 Pac-12) stormed back, turning two turnovers and a blocked punt into three touchdowns.

Jon Mora got the rally started with a field goal. Marion Grice, who ran for 156 yards, scored his third touchdown on a 4-yard run to tie the game after Keelan Johnson forced Arizona quarterback Matt Scott to fumble.

Kevin Ayers blocked a punt to set up Cameron Marshall for an 8-yard touchdown to give Arizona State the lead. Robert Nelson then returned an interception 66 yards before Michael Eubank's 1-yard touchdown made it 41-27.

Even after Scott hit David Richards on a 17-yard touchdown pass in the final two minutes to cut the lead to seven, the Sun Devils didn't let Arizona come up with the onside kick and ran out the clock.

The memorable victory ensured Arizona State's first winning season since 2007 and gave Graham a leg up on Rodriguez in the 85-game series' first game between new coaches since Arizona's John Mackovic beat ASU's Dirk Koetter in 2001.

``We were down by 10, we kept battling, kept making plays, forced a couple of turnovers; then what? We won the game,'' said Arizona State senior linebacker Brandon Magee, who had 17 tackles. ``It happened just like that.''

The Wildcats (7-5, 4-5) thought they had it won.

Trailing by eight at halftime, Arizona went up 10 in the third quarter after Scott hit Aaron Hill on a 22-yard touchdown and Garic Wharton on a 40-yarder, and John Bonano kicked a 23-yard field goal.

The Wildcats just couldn't hold on.

Arizona gave up the blocked punt in the fourth quarter, and Scott had two of his four turnovers - an interception and a fumble - in the final nine minutes to let the game slip away.

Ka'Deem Carey ran for 172 yards and a touchdown, and Scott threw for 230 yards and three touchdowns with three interceptions and the crucial fumble.

A heated rivalry to begin with, the Territorial Cup took on added meaning this season with new coaches trying to get a head start on each other.

After an unsuccessful stint at Michigan, Rodriguez brought gas-it-all-the-time offense to the desert, hoping to turn around a program that had fallen off hard the previous couple of seasons.

Even without much depth on his roster, Rodriguez's debut has been a success: Seven wins, two over Top 25 teams, and bowl eligibility in his first season.

Just 90 minutes up Interstate 10 in Tempe, Graham put his mark on the Sun Devils with his no-nonsense approach and high-octane offense. Arizona State got off to a great start, winning five of its first six games, then rallied from a four-game losing streak to become bowl eligible by beating Washington State last weekend.

For all they accomplished, Friday night's game was the biggest of the season. Bragging rights, an advantage in recruiting, a boost for fans and alumni - plenty was riding on this game.

``This game was everything,'' Graham said.

It took a while to get going.

The only player on either team to get much going early, Carey passed Trung Canidate's single-season school record of 1,602 yards rushing, set in 1999, on Arizona's second drive, then launched himself over Arizona State safety Alden Darby for a 1-yard touchdown run to cap it.

Bogged down early, Arizona State got going by picking off two of Scott's passes. Grice followed both with touchdowns: a nifty 52-yard run and a score from 3 yards out to help the Sun Devils to a 14-9 halftime lead.

After that came the fireworks, the rivals trading big swings of momentum by combining for 52 points, 502 yards of offense and disparate emotions from teams that wanted this game more than any other this season.

``This was a high-energy game, and I didn't expect it to be any different,'' Arizona nose guard Tevin Hood said. ``There were a lot of momentum shifts, and that really played a big part of the game.''

The Sun Devils got the biggest shift, in the game and for the rivalry's two new coaches.